A roller coaster moves 200 ft horizontally and then rises

A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30.0 above the horizontal. Next, it travels 135 ft at an angle of 40.0 below the horizontal. Use graphical techniques to nd the roller coasters displacement from its starting point to the end of this movement.

An airplane ies 200km due west from city A to city B and then 300km in the direction of 30.0 north of west from city B to city C. (a) In straight-line distance, how far is city C from city A? (b) Relative to city A, in what direction is city C?

A man lost in a maze makes three consecutive displacements so that at the end of his travel he is right back where he started. The rst displacement is 8.00 m westward, and the second is 13.0 m northward. Use the graphical method to nd the magnitude and direction of the third displacement.

A jogger runs 100 m due west, then changes direction for the second leg of the run. At the end of the run, she is 175 m away from the starting point at an angle of 15.0 north of west. What were the direction and length of her second displacement? Use graphical techniques.

A plane ies from base camp to lake A, a distance of 280 km at a direction of 20.0 north of east. After dropping off supplies, the plane ies to lake B, which is 190 km and 30.0 west of north from lake A. Graphically determine the distance and direction from lake B to the base camp.

Vector has a magnitude of 8.00 units and makes an angle of 45.0 with the positive x-axis. Vector also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods, nd (a) the vector sum  and (b) the vector difference 

Vector is 3.00units in length and points along the positive x-axis. Vector is 4.00units in length and points along the negative y-axis. Use graphical methods to nd the magnitude and direction of the vectors (a)  and (b)  .

Each of the displacement vectors and shown in Figure P3.8 has a magnitude of 3.00m. Graphically nd (a)  , (b)  , (c)  , and (d)  2.

A golfer takes two putts to get his ball into the hole once he is on the green. The rst putt displaces the ball 6.00 m east, the second 5.40 m south. What displacement would have been needed to get the ball into the hole on the rst putt?

A person walks 25.0 north of east for 3.10 km. How far would the person walk due north and due east to arrive at the same location?

A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and then 6.00 blocks east. (a) What is her resultant displacement? (b) What is the total distance she travels?

While exploring a cave, a spelunker starts at the entrance and moves the following distances: 75.0m north, 250m east, 125m at an angle 30.0 north of east, and 150m south. Find the resultant displacement from the cave entrance.

A vector has an x-component of 25.0 units and a y-component of 40.0 units. Find the magnitude and direction of the vector.

A quarterback takes the ball from the line of scrimmage, runs backwards for 10.0 yards, then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a 50.0-yard forward pass straight downeld, perpendicular to the line of scrimmage. What is the magnitude of the footballs resultant displacement?

The eye of a hurricane passes over Grand Bahama Island in a direction 60.0 north of west with a speed of 41.0 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 25.0 km/h. How far from Grand Bahama is the hurricane 4.50 h after it passes over the island?

A small map shows Atlanta to be 730 miles in a direction 5 north of east from Dallas. The same map shows that Chicago is 560 miles in a direction 21 west of north from Atlanta. Assume a at Earth, and use the given information to nd the displacement from Dallas to Chicago.

A commuter airplane starts from an airport and takes the route shown in Figure P3.17. The plane rst ies to city A, located 175 km away in a direction 30.0 north of east. Next, it ies for 150 km 20.0 west of north, to city B. Finally, the plane ies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.

The helicopter view in Figure P3.18 shows two people pulling on a stubborn mule. Find (a) the single force that is equivalent to the two forces shown and (b) the force that a third person would have to exert on the mule to make the net force equal to zero. The forces are measured in units of newtons (N).

A man pushing a mop across a oor causes the mop to undergo two displacements. The rst has a magnitude of 150 cm and makes an angle of 120 with the positive x-axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35.0 to the positive x-axis. Find the magnitude and direction of the second displacement.

An airplane starting from airport A ies 300 km east, then 350 km at 30.0 west of north, and then 150 km north to arrive nally at airport B. (a) The next day, another plane ies directly from A to B in a straight line. In what direction should the pilot travel in this direct ight? (b) How far will the pilot travel in the ight? Assume there is no wind during either ight.

Long John Silver, a pirate, has buried his treasure on an island with ve trees located at the following points: A (30.0 m, 20.0 m), B (60.0 m, 80.0 m), C (10.0 m, 10.0 m), D (40.0 m, 30.0 m), and E (70.0 m, 60.0 m). All of the points are measured relative to some origin, as in Figure P3.21. Long Johns map instructs you to start at A and move toward B, but cover only one-half the distance between A and B. Then move toward C, covering one-third the distance between your current location and C. Then move toward D, covering one-fourth the distance between where you are and D. Finally, move toward E, covering one-fth the distance between you and E, stop, and dig. (a) What are the coordinates of the point where the pirates treasure is buried? (b) Rearrange the order of the trees for instance, B (30m, 20m), A (60m, 80m), E (10m, 10m), C (40m, 30m), and D (70m, 60m)and repeat the calculation to show that the answer does not depend on the order.

One of the fastest recorded pitches in major-league baseball, thrown by Billy Wagner in 2003, was clocked at 101.0 mi/h (Fig. P3.22). If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached home plate, 60.5 ft away?

A peregrine falcon is the fastest bird, ying at a speed of 200 mi/h. Nature has adapted the bird to reach such a speed by placing bafes in its nose to prevent air from rushing in and slowing it down. Also, the birds eyes adjust their focus faster than the eyes of any other creature, so the falcon can focus quickly on its prey. Assume that a peregrine falcon is moving horizontally at its top speed at a height of 100 m above the ground when it brings its wings into its sides and begins to drop in free fall. How far will the bird fall vertically while traveling horizontally a distance of 100 m?

A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above a at, horizontal beach, as shown in Figure P3.24. How long after being released does the stone strike the beach below the cliff? With what speed and angle of impact does the stone land?

The best leaper in the animal kingdom is the puma, which can jump to a height of 12 ft when leaving the ground at an angle of 45. With what speed, in SI units, must the animal leave the ground to reach that height?

Tom the cat is chasing Jerry the mouse across the surface of a table 1.5 m above the oor. Jerry steps out of the way at the last second, and Tom slides off the edge of the table at a speed of 5.0 m/s. Where will Tom strike the oor, and what velocity components will he have just before he hits?

A tennis player standing 12.6 m from the net hits the ball at 3.00 above the horizontal. To clear the net, the ball must rise at least 0.330 m. If the ball just clears the net at the apex of its trajectory, how fast was the ball moving when it left the racquet?

An artillery shell is red with an initial velocity of 300 m/s at 55.0 above the horizontal. To clear an avalanche, it explodes on a mountainside 42.0 s after ring. What are the x- and y-coordinates of the shell where it explodes, relative to its ring point?

A brick is thrown upward from the top of a building at an angle of 25 to the horizontal and with an initial speed of 15 m/s. If the brick is in ight for 3.0 s, how tall is the building?

A placekicker must kick a football from a point 36.0 m (about 39 yd) from the goal, and the ball must clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a velocity of 20.0 m/s at an angle of 53 to the horizontal. (a) By how much does the ball clear or fall short of clearing the crossbar? (b) Does the ball approach the crossbar while still rising or while falling?

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0 below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 4.00 m/s2 for a distance of 50.0 m to the edge of the cliff, which is 30.0 m above the ocean. Find (a) the cars position relative to the base of the cliff when the car lands in the ocean and (b) the length of time the car is in the air.

A reman 50.0 m away from a burning building directs a stream of water from a ground-level re hose at an angle of 30.0 above the horizontal. If the speed of the stream as it leaves the hose is 40.0 m/s, at what height will the stream of water strike the building?

A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.0 above the horizontal. The projectile lands on a hillside 4.00 s later. Neglect air friction. (a) What is the projectiles velocity at the highest point of its trajectory? (b) What is the straight-line distance from where the projectile was launched to where it hits its target?

A soccer player kicks a rock horizontally off a 40.0-m-high cliff into a pool of water. If the player hears the sound of the splash 3.00 s later, what was the initial speed given to the rock? Assume the speed of sound in air to be 343 m/s.

A jet airliner moving initially at 300 mi/h due east enters a region where the wind is blowing at 100 mi/h in a direction 30.0 north of east. What is the new velocity of the aircraft relative to the ground?

A boat moves through the water of a river at 10 m/s relative to the water, regardless of the boats direction. If the water in the river is owing at 1.5 m/s, how long does it take the boat to make a round trip consisting of a 300-m displacement downstream followed by a 300-m displacement upstream?

A Chinook (King) salmon (Genus Oncorynchus) can jump out of water with a speed of 6.26 m/s. (See Problem 4.9, page 109 for an investigation of how the sh can leave the water at a higher speed than it can swim underwater.) If the salmon is in a stream with water speed equal to 1.50 m/s, how high in the air can the sh jump if it leaves the water traveling vertically upwards relative to the Earth?

A river ows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.0 m/s due north relative to the water. (a) What is the velocity of the boat relative to the shore? (b) If the river is 300 m wide, how far downstream has the boat moved by the time it reaches the north shore?

A rowboat crosses a river with a velocity of 3.30 mi/h at an angle 62.5 north of west relative to the water. The river is 0.505 mi wide and carries an eastward current of 1.25 mi/h. How far upstream is the boat when it reaches the opposite shore?

Suppose a Chinook salmon needs to jump a waterfall that is 1.50 m high. If the sh starts from a distance 1.00 m from the base of the ledge over which the waterfall ows, nd the x- and y-components of the initial velocity the salmon would need to just reach the ledge at the top of its trajectory. Can the sh make this jump? (Remember that a Chinook salmon can jump out of the water with a speed of 6.26 m/s.)

How long does it take an automobile traveling in the left lane of a highway at 60.0 km/h to overtake (become even with) another car that is traveling in the right lane at 40.0 km/h when the cars front bumpers are initially 100 m apart?

A science student is riding on a atcar of a train traveling along a straight horizontal track at a constant speed of 10.0 m/s. The student throws a ball along a path that she judges to make an initial angle of 60.0 with the horizontal and to be in line with the track. The students professor, who is standing on the ground nearby, observes the ball to rise vertically. How high does the ball rise?

A particle undergoes two displacements. The rst has a magnitude of 150 cm and makes an angle of 120.0 with the positive x-axis. The resultant of the two displacements is 140 cm, directed at an angle of 35.0 to the positive x-axis. Find the magnitude and direction of the second displacement.

Find the sum of these four vector forces: 12.0 N to the right at 35.0 above the horizontal, 31.0 N to the left at 55.0 above the horizontal, 8.40 N to the left at 35.0 below the horizontal, and 24.0 N to the right at 55.0 below the horizontal. (Hint: N stands for newton, the SI unit of force. The component method allows the addition of any vectorsforces as well as displacements and velocities. Make a drawing of this situation, and select the best axes for x and y so that you have the least number of components.)

A car travels due east with a speed of 50.0 km/h. Rain is falling vertically with respect to Earth. The traces of the rain on the side windows of the car make an angle of 60.0 with the vertical. Find the velocity of the rain with respect to (a) the car and (b) Earth.

You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity at an angle  with respect to the horizontal. Let the building be 50.0 m tall, the initial horizontal velocity be 9.00 m/s, and the initial vertical velocity be 12.0 m/s. Choose your coordinates such that the positive y-axis is upward, the x-axis is to the right, and the origin is at the point where the ball is released. (a) With these choices, nd the balls maximum height above the ground, and the time it takes to reach the maximum height. (b) Repeat your calculations choosing the origin at the base of the building.

Towns A and B in Figure P3.47 are 80.0 km apart. A couple arranges to drive from town A and meet a couple driving from town B at the lake, L. The two couples leave simultaneously and drive for 2.50 h in the directions shown. Car 1 has a speed of 90.0 km/h. If the cars arrive simultaneously at the lake, what is the speed of car 2?

A Chinook salmon has a maximum underwater speed of 3.58 m/s, but it can jump out of water with a speed of 6.26 m/s. To move upstream past a waterfall, the salmon does not need to jump to the top of the fall, but only to a point in the fall where the water speed is less than 3.58 m/s; it can then swim up the fall for the remaining distance. Because the salmon must make forward progress in the water, lets assume that it can swim to the top if the water speed is 3.00 m/s. If water has a speed of 1.50 m/s as it passes over a ledge, how far below the ledge will the water be moving with a speed of 3.00 m/s? (Note that water undergoes projectile motion once it leaves the ledge.) If the salmon is able to jump vertically upward from the base of the fall, what is the maximum height of waterfall that the salmon can clear?

A rocket is launched at an angle of 53.0 above the horizontal with an initial speed of 100 m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 30.0 m/s2. At this time, its engines fail and the rocket proceeds to move as a projectile. Find (a) the maximum altitude reached by the rocket, (b) its total time of ight, and (c) its horizontal range.

Two canoeists in identical canoes exert the same effort paddling and hence maintain the same speed relative to the water. One paddles directly upstream (and moves upstream), whereas the other paddles directly downstream. With downstream as the positive direction, an observer on shore determines the velocities of the two canoes to be 1.2 m/s and 2.9 m/s, respectively. (a) What is the speed of the water relative to the shore? (b) What is the speed of each canoe relative to the water?

If a person can jump a maximum horizontal distance (by using a 45 projection angle) of 3.0 m on Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6 and g  9.80 m/s2? Repeat for Mars, where the acceleration due to gravity is 0.38g.

A daredevil decides to jump a canyon. Its walls are equally high and 10 m apart. He takes off by driving a motorcycle up a short ramp sloped at an angle of 15. What minimum speed must he have in order to clear the canyon?

(a) Vector is in the rst quadrant of a Cartesian coordinate system. What is the sign of the x-component of ? What is the sign of the y-component? (b) Vector is in the second quadrant of a Cartesian coordinate system. What is the sign of the x-component of ? What is the sign of the y-component? (c) The vector sum  . Choose the correct ll-in-the-blank answer from (i) must be in either the rst or the second quadrant or (ii) could be in any quadrant. (d) Let  30 m at an angle of 30 from the positive x-axis and  20 m at an angle of 40 from the negative x-axis. Test your predictions of parts (a) through (c).

A boy and a girl are tossing an apple back and forth between them. Figure P3.54 shows one path the apple follows when watched by an observer looking on from the side. The apple is moving from left to right. Five points are marked on the path. Ignore air resistance. (a) Make a copy of this gure. At each of the marked points, draw an arrow that indicates the magnitude and direction of the apples velocity when it passes through that point. (b) Make a second copy of the gure. This time, at each marked point, place an arrow indicating the magnitude and direction of any acceleration the apple exhibits at that point.

A home run is hit in such a way that the baseball just clears a wall 21 m high, located 130 m from home plate. The ball is hit at an angle of 35 to the horizontal, and air resistance is negligible. Find (a) the initial speed of the ball, (b) the time it takes the ball to reach the wall, and (c) the velocity components and the speed of the ball when it reaches the wall. (Assume that the ball is hit at a height of 1.0 m above the ground.)

A ball is thrown straight upward and returns to the throwers hand after 3.00 s in the air. A second ball is thrown at an angle of 30.0 with the horizontal. At what speed must the second ball be thrown so that it reaches the same height as the one thrown vertically?

A quarterback throws a football toward a receiver with an initial speed of 20 m/s at an angle of 30 above the horizontal. At that instant, the receiver is 20 m from the quarterback. In what direction and with what constant speed should the receiver run in order to catch the football at the level at which it was thrown?

A 2.00-m-tall basketball player is standing on the oor 10.0 m from the basket, as in Figure P3.58. If he shoots the ball at a 40.0 angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 m.

In a very popular lecture demonstration, a projectile is red at a falling target as in Figure P3.59. The projectile leaves the gun at the same instant that the target is dropped from rest. Assuming that the gun is initially aimed at the target, show that the projectile will hit the target. (One restriction of this experiment is that the projectile must reach the target before the target strikes the oor.)

Figure P3.60 illustrates the difference in proportions between the male (m) and female (f) anatomies. The displacements 1m and 1f from the bottom of the feet to the navel have magnitudes of 104 cm and 84.0 cm, respectively. The displacements 2m and 2f have magnitudes of 50.0 cm and 43.0 cm, respectively. (a) Find the vector sum of the displacements 1 and 2 in each case. (b) The male gure is 180 cm tall, the female 168 cm. Normalize the displacements of each gure to a common height of 200 cm, and re-form the vector sums as in part (a). Then nd the vector difference between the two sums.

By throwing a ball at an angle of 45, a girl can throw the ball a maximum horizontal distance R on a level eld. How far can she throw the same ball vertically upward? Assume that her muscles give the ball the same speed in each case. (Is this assumption valid?)

A projectile is red with an initial speed v0 at an angle  0 to the horizontal, as in Figure 3.14. When it reaches its peak, the projectile has (x, y) coordinates given by (R/2, h), and when it strikes the ground, its coordinates are (R, 0), where R is called the horizontal range. (a) Show that the projectile reaches a maximum height given by (b) Show that the horizontal range of the projectile is given by

A hunter wishes to cross a river that is 1.5 km wide and ows with a speed of 5.0 km/h parallel to its banks. The hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time necessary for crossing?

A water insect maintains an average position on the surface of a stream by darting upstream (against the current) then drifting downstream (with the current) to its original position. The current in the stream is 0.500 m/s relative to the shore, and the insect darts upstream 0.560 m (relative to a spot on shore) in 0.800 s during the rst part of its motion. Take upstream as the positive direction. (a) Determine the velocity of the insect relative to the water (i) during its dash upstream and (ii) during its drift downstream. (b) How far upstream relative to the water does the insect move during one cycle of its motion? (c) What is the average velocity of the insect relative to the water?

A daredevil is shot out of a cannon at 45.0 to the horizontal with an initial speed of 25.0 m/s. A net is positioned a horizontal distance of 50.0 m from the cannon. At what height above the cannon should the net be placed in order to catch the daredevil?

Chinook salmon are able to move upstream faster by jumping out of the water periodically; this behavior is called porpoising. Suppose a salmon swimming in still water jumps out of the water with a speed of 6.26 m/s at an angle of 45, sails through the air a distance L before returning to the water, and then swims a distance L underwater at a speed of 3.58 m/s before beginning another porpoising maneuver. Determine the average speed of the sh.

A student decides to measure the muzzle velocity of a pellet shot from his gun. He points the gun horizontally. He places a target on a vertical wall a distance x away from the gun. The pellet hits the target a vertical distance y below the gun. (a) Show that the position of the pellet when traveling through the air is given by y  Ax2, where A is a constant. (b) Express the constant A in terms of the initial (muzzle) velocity and the free-fall acceleration. (c) If x  3.00 m and y  0.210 m, what is the initial speed of the pellet?

A sailboat is heading directly north at a speed of 20 knots (1 knot  0.514 m/s). The wind is blowing towards the east with a speed of 17 knots. Determine the magnitude and direction of the wind velocity as measured on the boat. What is the component of the wind velocity in the direction parallel to the motion of the boat? (See Problem 4.54 for an explanation of how a sailboat can move into the wind.)

Instructions for nding a buried treasure include the following: Go 75 paces at 240, turn to 135 and walk 125 paces, and then travel 100 paces at 160. Determine the resultant displacement from the starting point.

When baseball outelders throw the ball, they usually allow it to take one bounce, on the theory that the ball arrives at its target sooner that way. Suppose that, after the bounce, the ball rebounds at the same angle  that it had when it was released (as in Fig. P3.70), but loses half its speed. (a) Assuming that the ball is always thrown with the same initial speed, at what angle  should the ball be thrown in order to go the same d istance D with one bounce as a ball thrown upward at 45.0 with no bounce? (b) Determine the ratio of the times for the one-bounce and no-bounce throws.

One strategy in a snowball ght is to throw a snowball at a high angle over level ground. Then, while your opponent is watching that snowball, you throw a second one at a low angle timed to arrive before or at the same time as the rst one. Assume that both snowballs are thrown with a speed of 25.0 m/s. The rst is thrown at an angle of 70.0 with respect to the horizontal. (a) At what angle should the second snowball be thrown to arrive at the same point as the rst? (b) How many seconds later should the second snowball be thrown after the rst in order for both to arrive at the same time?

A dart gun is red while being held horizontally at a height of 1.00 m above ground level and while it is at rest relative to the ground. The dart from the gun travels a horizontal distance of 5.00 m. A college student holds the same gun in a horizontal position while sliding down a 45.0 incline at a constant speed of 2.00 m/s. How far will the dart travel if the student res the gun when it is 1.00 m above the ground?

The determined Wile E. Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of Acme power roller skates, which provide a constant horizontal acceleration of 15 m/s2, as shown in Figure P3.73. The coyote starts off at rest 70 m from the edge of a cliff at the instant the roadrunner zips by in the direction of the cliff. (a) If the roadrunner moves with constant speed, nd the minimum speed the roadrunner must have in order to reach the cliff before the coyote. (b) If the cliff is 100 m above the base of a canyon, nd where the coyote lands in the canyon. (Assume that his skates are still in operation when he is in ight and that his horizontal component of acceleration remains constant at 15 m/2.)

Take three steps, turn 90, and then walk four steps. Now count the number of steps it takes to walk in a straight line back to your starting point. Verify your result mathematically.

For this investigation, you need to be outside with a small ball such as a tennis ball and a wristwatch with a second hand. Throw the ball vertically upward as hard as you can, and nd the initial speed of your throw and the approximate maximum height of the ball solely with the use of your wristwatch. What happens when you throw the ball at some angle other than 90? Does this change the time of ight? Can you still determine the maximum height and initial speed? Give careful explanations for your answers. Your co-worker can eyeball the maximum height by standing at a distance and noting the angle.

Using as projectiles the drops of water spraying from a garden hose at ground level, test the statement that the maximum range occurs when the angle of projection is 45. As an additional part of this experiment, hold the hose horizontally above the ground and have your coworker position a marker at the location where the water strikes the ground. Increase the angle of inclination by about 10, and record the strike position again. Repeat until you have reached an angle of about 75. Note the pattern produced. Are there two angles at which the range is the same? Explain the reasoning behind your observations.

Use a chessboard as a coordinate system, with the intersection of the lines on the board as the positions of the coordinates. Select an origin for your coordinate system and, on index cards, write down several vector displacements that are at right angles to one another. For example, displacement 1 might be a movement of four units to the right, displacement 2 an upward movement of six units, and so forth. Continue this for a total of seven or eight movements until you end up at some particular location on the chessboard. Let your co-worker start at the origin and follow your vector directions to see whether he or she arrives at the expected nal location. Now shufe the cards and repeat the experiment. Does the order of the displacements make any difference as to where you eventually end up?

Roll a ball off a table. At the very instant the rolling ball leaves the table, drop a second ball from the same height above the oor. (Doing this will require a sharp eye and good reexes!) Do the two balls hit the oor at the same time? Try varying the speed at which you roll the ball off the table. Does this change affect the time at which the balls strike the oor? Finally, roll one of the balls down an incline, and drop the other ball from the base of the incline at the instant the rst ball leaves the slope. Which of these balls hits the oor rst in this situation? Explain the reasoning behind your observations.